The Black Sticks were found guilty of wastefulness in their own defensive area, as Nick Haig lost possession in a dangerous position. Questions were asked about the legality of the dispossession, but it led to a shot at goal which hit Kane Russell - situated behind the goalkeeper - resulting in a penalty.
Indian set-piece expert Rhupinder Pal Singh struck a faultless penalty into the bottom left corner to give India the lead, and they continued to look the more threatening side.
Black Sticks goalie George Enersen was forced into a good save soon after as India started to take the ascendancy, striking eight first-half shots on target to New Zealand's two.
The Black Sticks began to show promising signs in the third period, with only a great pad save from Indian custodian Akash Chikte denying a sprawling Matt Rees-Gibbs at the back post.
They eventually found their equaliser as Nick Ross deftly turned in a cross from Hugo Inglis, and then made that two goals in two minutes as Jacob Smith turned one home after a goalmouth scramble.
Inglis went from provider to finisher with a well-worked move from a penalty corner for what seemed to be the clinching goal, but India weren't done as Rhupinder immediately dragged a goal back.
A draw would have seen India make the final, so they pulled their goalkeeper in the dying minutes, holding a significant numbers advantage on New Zealand, who were down to 10 men after Russell was shown a green card.
India thought they had their late equaliser but the whistle had blown before the ball crossed the line, and they had one last chance when they won a penalty corner with two seconds left on the clock.
Rhupinder stepped up to be the hero, but his shot was saved and the Black Sticks advance.
New Zealand 3 (Nick Ross, Jacob Smith, Hugo Inglis goals)
India 2 (Rhupinder Pal Singh 2 goals)
Halftime: 0-1
